HW Stereotctic Trgeting We re bout to perform stereotctic rdiosurgery with the Gmm Knife under CT guidnce. We instrument the ptient with bse ring nd for CT scnning we ttch fiducil cge (FC). Above: bse ring ttched to the hed (left imge), fiducil cge ttched to the bse ring (middle imge). The Gmm Knife (right imge) is ligned with the fiducil cge nd in the home position, center of the cge, center of the helmet (i.e. center of the Gmm knife) coincide. T CT The bse ring is ttched to the scnner tble mechniclly, so tht the CT imges nd fiducil cge re ligned without rottion. The surgeon selects the CT imge tht shows the trget (T CT ) point. This CT slice lso intersect the rdio-opque fiducil rods comprising the FC, yielding nine mrker points. We segment the mrker points in the CT imge. The imge in the left shows specil cse, when the CT nd FC re ligned without rottion. Generlly, the CT nd FC re slnted rbitrrily. The tsk before you is to develop progrm tht clcultes the T CT trget point in fiducil cge frme to yield T FC. In order to tret the tumor, we will trnslte the ptient inside the helmet by this T FC so the trget point flls in the center of the helmet. 1
Fiducil cge geometry The shpe of one Z motif is shown in the figure. (A relistic vlue for the length of the stright fiducil rod is =10cm.) ANTERIOR y 2 /2 /2 4 5 6 RIGHT 3 7 2 LEFT 2 8 /2 x 1 9 /2 POSTERIOR 2
Fiducil cge geometry (continued) ANT y x LEFT Z This figure explins the rrngement if the slnted fiducil rods. The Z on the left side of the ptient is drwn dotted, becuse it is hidden in this view. 3
CT Imge geometry FOVX FOVY FOVY RIGHT y LEFT x FOVX Horizontl field of view FOVX (typicl vlue 250 mm) Verticl field of view FOVY (typicl vlue 250 mm) 4
Trnsformer (35 pts) In n ctul tretment, the neurosurgeon selects the CT imge tht contins the trget point (P CT ) for biopsy nd mrks the this point in the CT imge. We segment the mrks of the fiducil rods in the CT imges. (We converted them from pixels to metric coordintes, to del with scling.) You must develop progrm tht produces coordinte frme trnsformtion tht tkes P CT trget point from CT coordintes to P FC fiducil cge coordintes. INPUT: Vector of fiducil points in CT coordintes OUTPUT: Frme trnsformtion M s 4x4 homogeneous mtrix TESTING: Generte 3 esy to see-through ground truth exmples on pper. Explin the testing process nd the construction of test cses. Explin wht you expect to get nd compre to wht your progrm is outputting. 5
Simultor (35 pts) Write dt Simultor progrm to generte fiducil mrker points in CT coordintes. The generl ide is the following: Assume tht the CT nd FC frmes re identicl Apply known ground truth trnsformtion to the fiducil cge by trnsforming ech fiducil rod. Clculte the intersection points between the CT slice nd the trnsformed fiducil cge in CT coordintes. USEFUL TIPS: Write up the vector eqution of the rods in fiducil cge coordinte system. Write up the eqution of the CT plne Trnsform the cge Intersect the CT plne with the rods. The result will be mrker points in CT coordintes. INPUT: Ground truth trnsformtion s 4x4 homogeneous trnsformtion mtrix OUTPUT: F CT vector of fiducil points in CT coordinte TESTING: Generte 3 esy to see-through ground truth exmples on pper. Explin the testing process nd the construction of test cses. Explin wht you expect to get nd compre to wht your progrm is outputting. 6
Anlyzer (30 pts) Write progrm to Generte M=10 rndom ground truth frme trnsformtions between CT nd FC. Look t the CT imge in pge 2 nd 4 nd set limit on your rndom ground truth trnsformtions so the fiducil mrkers do not fll off the CT imge. Cll your simultor to generte the fiducil mrker points in CT coordintes. Introduce FLE by spoiling the fiducil mrker loctions by some rndom locliztion error less thn some FLEmx. Wht kind of rndomiztion you choose nd why? Include this in the code comments. Generte N=30 rndom trget ground truth points inside the CT imge within in 5cm rdius from the center of the imge. Cll your Trnsform progrm to produce frme trnsformtion between CT frme nd FC frme Step FLEmx from 0 to 5mm, in 1mm increments. Compute FRE (verge, std) Compute TRE (verge, std) Plot FRE nd TRE s function of FLEmx Anlyze the result from the perspective of the rdiosurgery tretment sfety if we require less thn 3mm TRE for the tretment. 7
GENERAL RULES Red the online syllbus crefully for generl instructions on the submission of ssignments. Alwys explin how you solve problem. Use drwings, mth formuls, text, block digrm, pseudo code - nything tht you find them pproprite to convey your ides. I must know tht you understnd wht you re doing nd I must be ble to follow your resoning. Depending on the qulity nd depth of your resoning nd discussion or results you my pick (or lose) lots of points. Write proper heder nd richly comment your code. There is no such thing s too much comment. Good style nd netness will ern you vluble points. The lck of these will cuse reduction. Use deciml digits sensibly nd consider wht is precision is prcticl for the given problem. Generlly, resolution much finer thn 1 mm is not prcticlly chievble, so use 0.1 mm s your. Use integer or deciml point formt in your outputs. No exponentil number formt! Test ech module fully nd construct severl test cses with known ground-truth nswer. Construct the exmples on pper, explin the result tht you expect, then run the exmple through the code nd show tht your progrm is correct it produces the ground truth you pre-computed. Write testing m file(s) for ech module or problem. Cpture the output, to show tht your progrm does wht it is supposed to do. Mke plots whenever it is requested or mkes sense. Add explntion text s you see it useful. Use MATLAB routines for recurring tsks. Submit the m files nd the cptured output file, s well s ny drwing, or supplementl informtion you feel relevnt. Hve fun! 8